| 186 is a composite number. |
| Factor pairs: 186 = 1 x 186, 2 x 93, 3 x 62, 6 x 31 |
| Factors of 186: 1, 2, 3, 6, 31, 62, 93, 186 |
| Prime factorization: 186 = 2 x 3 x 31 |
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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-28
| 185 is a composite number. |
| Factor pairs: 185 = 1 x 185 or 5 x 37 |
| Factors of 185: 1, 5, 37, 185 |
| Prime factorization: 185 = 5 x 37 |
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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
| 184 is a composite number. |
| Factor pairs: 184 = 1 x 184, 2 x 92, 4 x 46, or 8 x 23 |
| Factors of 184: 1, 2, 4, 8, 23, 46, 92, 184 |
| Prime factorization: 184 = 2 x 2 x 2 x 23, which can be written (2^3) x 23 |
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Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
| 183 is a composite number. |
| Factor pairs: 183 = 1 x 183 or 3 x 61 |
| Factors of 183: 1, 3, 61, 183 |
| Prime factorization: 183 = 3 x 61 |
Notice this for 183: 1 + 8 + 3 = 12 which is a multiple of 3, so 183 is also a multiple of 3.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
| 182 is a composite number. |
| Factor pairs: 182 = 1 x 182, 2 x 91, 7 x 26, or 13 x 14 |
| Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182 |
| Prime factorization: 182 = 2 x 7 x 13 |
Notice this for 182: 18 – (2 x 2) = 18 – 4 = 14, a multiple of 7, so 182 can be evenly divided by 7.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
A Logical Approach to FIND THE FACTORS: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row). Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.
How do we know that 181 is a prime number? If 181 were not a prime number, then it would be divisible by at least one prime number less than or equal to √181 ≈ 13.5. Since 181 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 181 is a prime number.
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
Excel file of puzzles and previous week’s factor solutions: 10 Factors 2014-07-21
| 180 is a composite number. |
| Factor pairs: 180 = 1 x 180, 2 x 90, 3 x 60, 4 x 45, 5 x 36, 6 x 30, 9 x 20, 10 x 18, or 12 x 15 |
| Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 |
| Prime factorization: 180 = 2 x 2 x 3 x 3 x 5 which can be written 180 = (2^2) x (3^2) x 5 |
180 has nine factor pairs. One of the factor pairs adds up to 41, and another one subtracts to 41. If you can identify those two factor pairs, then you can solve this puzzle!
There are 180 degrees in a triangle, and a straight angle is 180 degrees.
180 is the hypotenuse of a Pythagorean triple:
108-144-180, which is (3-4-5) times 36.
How do we know that 179 is a prime number? If 179 were not a prime number, then it would be divisible by at least one prime number less than or equal to √179 ≈ 13.4. Since 179 cannot be divided evenly by 2, 3, 5, 7, 11, or 13, we know that 179 is a prime number.
Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-14
| 178 is a composite number. |
| Factor pairs: 178 = 1 x 178 or 2 x 89 |
| Factors of 178: 1, 2, 89, 178 |
| Prime factorization: 178 = 2 x 89 |
Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-14
| 177 is a composite number. |
| Factor pairs: 177 = 1 x 177, 3 x 59 |
| Factors of 177: 1, 3, 59, 177 |
| Prime factorization: 177 = 3 x 59 |
Here is a magic square made entirely of prime numbers:
What number do you get when you add up the numbers of any one of its rows, columns, or diagonals?
According to Wikipedia, you can’t get a smaller magic sum than 177 when all the numbers in the magic square are prime numbers. Wolfram MathWorld has several Prime Magic Squares of various dimensions up to 13 × 13. Two of the squares include the number 1, which is not a prime number but is sometimes permitted to be in a prime magic square because it is not a composite number.
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Excel file of puzzles and previous week’s factor solutions: 12 Factors 2014-07-14
